This follows by the same argument as p:lq-lim, observing that if \(\zeta \in \Omega ^*\)  is a path ending in an essential loop class \(\mathcal {L}\) , then \(\eta \in \Omega ^*_{\mathcal {L},\zeta }\)  if and only if \(\eta \in \Omega ^*\)  and \(\zeta \)  is a prefix of \(\eta \) .
That \(\tau _{\mathcal {L}}(q)=\tau _\mu (q)\)  for \(q\ge 0\)  follows by standard arguments (see, for example, [1]}).
